Unified study of $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ and $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ processes

Abstract

We perform a unified description of the experimental data of the ${\pi }^{+}{\pi }^{-}$ invariant mass spectra of $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}$, the ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ invariant mass spectra of $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$, and the ratio of branch fractions $\mathcal{B}[B_s^0\to X(3872)(K^{+}{K}^{-}{)}_{\mathrm{non}-\varphi }]/\mathcal{B}[B_s^0\to X(3872){\pi }^{+}{\pi }^{-})$. The strong final state interactions between the two pseudoscalars are taken into account using a parametrization fulfilling unitarity and analyticity. We find that there is universality in the coupling constants for $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}$ and $B_s^0\to J/\psi {\pi }^{+}{\pi }^{-}$ processes. While the couplings of $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}$ are about half of magnitude smaller than the couplings of $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}$, which indicates that the $X(3872)$ is different from a pure charmonium state. Furthermore, we find that the $f_0(1500)$ plays an important role in the $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}$ and the $B_s^0\to X(3872){\pi }^{+}{\pi }^{-}(K^{+}{K}^{-})$ processes, though the phase space of $B_s^0\to X(3872)f_0(1500)$ is small. Also we predict the ratio of branch fractions $\mathcal{B}[B_s^0\to \psi (2S)(K^{+}{K}^{-}{)}_{\mathrm{non}-\varphi }]/\mathcal{B}[B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}]$ and the $K^{+}{K}^{-}$ invariant mass distribution of $B_s^0\to \psi (2S)K^{+}{K}^{-}$.

Comments: 15 pages, 3 figures